# Quant Quiz

**(Directions: 1-5):**Study the following bar charts carefully and answer the questions asked below.

**Foreign Trade (Imports and Exports) by various countries**

**1. The ratio of the maximum exports to the minimum imports was closest to ?**

(a) 64

(b) 69

(c) 74

(d) 79

**2. How many countries exhibited a trade surplus ?**

(a) 5

(b) 3

(c) 4

(d) 6

**3. The total trade deficit/surplus for all the countries (together) was ?**

(a) 11286 surplus

(b) 11286 deficit

(c) 10286 deficit

(d) 10286 surplus

**4. The highest trade deficit was shown by which country ?**

(a) C

(b) G

(c) H

(d) L

**5. The ratio of exports to imports was highest for which country ?**

(a) I

(b) A

(c) J

(d) K

**6. If the sum of two numbers is 55 and the HCF and LCM of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:**

(a) 55/601

(b) 601/55

(c) 11/120

(d) 120/11

**7. A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?**

(a) 28 4/7 years

(b) 31 5/7 years

(c) 32 1/7 years

(d) None of these

**8. 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 cubic metre**

**, then the rise in the water level in the tank will be:**

(a) 20 cm

(b) 25 cm

(c) 35 cm

(d) 50 cm

**9. A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs.6500 for 6 months, B, Rs.8400 for 5 months and C, Rs.10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs.7400. Calculate the share of B in the profit.**

(a) Rs.1900

(b) Rs.2660

(c) Rs.2800

(d) Rs.2840

**10. 8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally?**

(a) 18 litres

(b) 24 litres

(c) 32 litres

(d) 42 litres

The value of maximum exports = 6045.

The value of minimum imports = 87.

Therefore, the required ratio (6045/8)= 69.48 = 69 (approximately).

Out of a total of 12 countries, 8 showed a deficit while 4 showed a surplus.

Exports= 25625

Imports= 36911

Sum of exports - Sum of imports = deficit (11286).

Visually its clear that L has the highest trade deficit.

I has a ratio of 4002/2744 = 1.45, which is the highest.

Let the numbers be a and b.

Then, a+b= 55 and ab= 5*120= 600.

So the required sum= (1/a)+ (1/b)= (a+b)/ab=55/600= 11/120

Required average= (67*2+35*2+6*3)/(2+2+3)

= (134+70+18)/(7)

= 222/7

= 31 5/7 years

Total volume of water displaced= (4*50) cubic metre= 200 cubic metre

Rise in water level = (200/40*20)m= 0.25m= 25cm.

For managing, A received = 5% of Rs.7400= Rs.370

Balance= Rs.(7400-370)= Rs.7030

Ratio of their investments= (6500*6):(8400*5):(10000*3)= 39000:42000:30000

= 13:14:10

So, B's share= Rs.[7030*(14/37)] = Rs.2660

Let the quantity of the wine in the cask originally be x litres.

Then, quantity of wine left in cask after 4 operations= [x{1-(8/x)^4}] litres

So, [x{1-(8/x)}^4]/x= 16/81

= [1-(8/x)]^4=(2/3)^4

= (x-8)/x=2/3

= 3x-24= 2x

= x=24

**Answers:**

**1. (b)**The value of maximum exports = 6045.

The value of minimum imports = 87.

Therefore, the required ratio (6045/8)= 69.48 = 69 (approximately).

**2. (c)**Out of a total of 12 countries, 8 showed a deficit while 4 showed a surplus.

**3. (b)**Exports= 25625

Imports= 36911

Sum of exports - Sum of imports = deficit (11286).

**4. (d)**Visually its clear that L has the highest trade deficit.

**5. (a)**I has a ratio of 4002/2744 = 1.45, which is the highest.

**6. (c)**Let the numbers be a and b.

Then, a+b= 55 and ab= 5*120= 600.

So the required sum= (1/a)+ (1/b)= (a+b)/ab=55/600= 11/120

**7. (b)**Required average= (67*2+35*2+6*3)/(2+2+3)

= (134+70+18)/(7)

= 222/7

= 31 5/7 years

**8. (b)**Total volume of water displaced= (4*50) cubic metre= 200 cubic metre

Rise in water level = (200/40*20)m= 0.25m= 25cm.

**9. (b)**For managing, A received = 5% of Rs.7400= Rs.370

Balance= Rs.(7400-370)= Rs.7030

Ratio of their investments= (6500*6):(8400*5):(10000*3)= 39000:42000:30000

= 13:14:10

So, B's share= Rs.[7030*(14/37)] = Rs.2660

**10. (b)**Let the quantity of the wine in the cask originally be x litres.

Then, quantity of wine left in cask after 4 operations= [x{1-(8/x)^4}] litres

So, [x{1-(8/x)}^4]/x= 16/81

= [1-(8/x)]^4=(2/3)^4

= (x-8)/x=2/3

= 3x-24= 2x

= x=24

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